7. Systems of Equations & Matrices

Determinants and Cramer's Rule

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Guided videos.

Learn with Patrick

Go to the course

Guided course

4:36

Determinants of 2×2 Matrices

Cramer's Rule - 2 Equations with 2 Unknowns

Determinants of 3×3 Matrices

Cramer's Rule - 3 Equations w/ 3 Unknowns

Additional 1 creators.

Learn with other creators

Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

05:08

Ex: Find the Value of a 4x4 Determinant Using Cofactor Expansion (with Zeros)

Evaluate the Determinant of a 4x4 Matrix

Determinant of a 4X4 Matrix

How To Find The Determinant of a 4x4 Matrix

The Organic Chemistry Tutor

1458

views

Practice this topic

Multiple Choice

Evaluate the determinant of the matrix.

138

views

Multiple Choice

Write each equation in standard form and use Cramer's Rule to solve the system.

$y=-3x+4$

$-2x=7y-9$

179

views

Multiple Choice

Evaluate the determinant of the matrix.

202

views

Multiple Choice

Solve the system of equations using Cramer's Rule.

$4x+2y+3z=6$

$x+y+z=3$

$5x+y+2z=5$

142

views

Multiple Choice

Write each equation in standard form and use Cramer's Rule to solve the system.

$y-9x=-3$

$-3x=4y-1$

141

views

Textbook Question

What is the value of ?

162

views

Textbook Question

Evaluate each determinant in Exercises 1–10. 5 7 2 3

183

views

Textbook Question

What expression in x represents ?

154

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 4 1 5 6

191

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 7 14 2 - 4

170

views

Textbook Question

What is the value of x if = 9?

139

views

Textbook Question

Evaluate each determinant. See Example 1.

148

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 5 - 1 - 2 - 7

160

views

Textbook Question

Evaluate each determinant in Exercises 1–10. - 5 - 1 - 2 - 7

160

views

Textbook Question

Evaluate each determinant. See Example 1.

159

views

Textbook Question

Evaluate each determinant in Exercises 1–10. 1/2 1/2 1/8 - 3/4

169

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. x + y = 7 x - y = 3

Evaluate each determinant. See Example 1.

147

views

Textbook Question

Evaluate each determinant. See Example 1.

137

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 12x + 3y = 15 2x - 3y = 13

194

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 12x + 3y = 15 2x - 3y = 13

194

views

Textbook Question

Evaluate each determinant. See Example 1.

148

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 4x - 5y = 17 2x + 3y = 3

199

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. x + 2y = 3 3x - 4y = 4

251

views

Textbook Question

Find the cofactor of each element in the second row of each matrix. See Example 2.

159

views

Textbook Question

Find the cofactor of each element in the second row of each matrix. See Example 2.

205

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 3x - 4y = 4 2x + 2y = 12

207

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 3x - 4y = 4 2x + 2y = 12

207

views

Textbook Question

Evaluate each determinant. See Example 3.

144

views

Textbook Question

For Exercises 11–22, use Cramer's Rule to solve each system. 2x = 3y + 2 5x = 51 - 4y

209

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 0 0 2 1 - 5 2 5 - 1

175

views

Textbook Question

Evaluate each determinant. See Example 3.

132

views

Textbook Question

Evaluate each determinant. See Example 3.

170

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 1 0 - 3 4 0 - 1 3 - 5

186

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 3 1 0 - 3 4 0 - 1 3 - 5

186

views

Textbook Question

Evaluate each determinant. See Example 3.

146

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 1 1 1 2 2 2 - 3 4 - 5

163

views

Textbook Question

In Exercises 23–30, use expansion by minors to evaluate each determinant. 0.5 7 5 0.5 3 9 0.5 1 3

178

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. - 3 4 - 5 5 - 2 0 8 - 1 3

202

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. - 3 4 - 5 5 - 2 0 8 - 1 3

202

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 1 5 6 1 4 5 1 9 10

185

views

Textbook Question

In Exercises 31–36, use the alternative method for evaluating third-order determinants on here to evaluate each determinant. 0.5 7 5 0.5 3 9 0.5 1 3

170

views

Textbook Question

Evaluate each determinant.

255

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 0 2x - y + z = - 1 - x + 3y - z = - 8

166

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 0 2x - y + z = - 1 - x + 3y - z = - 8

166

views

Textbook Question

Evaluate each determinant.

194

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. 4x - 5y - 6z = - 1 x - 2y - 5z = - 12 2x - y = 7

299

views

Textbook Question

Evaluate each determinant.

195

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + y + z = 4 x - 2y + z = 7 x + 3y + 2z = 4

225

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + 2z = 10 2y - z = - 5 2x + 3y = 13

256

views

Textbook Question

In Exercises 37–44, use Cramer's Rule to solve each system. x + 2z = 10 2y - z = - 5 2x + 3y = 13

256

views

Textbook Question

In Exercises 45–48, explain why the system of equations cannot be solved using Cramer's Rule. Then use Gaussian elimination to solve the system. 2x - 3y + 2z = 4 2x + 3y - 2z = 6 2x - 9y + 6z = 2

272

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

309

views

Textbook Question

In Exercises 45–48, explain why the system of equations cannot be solved using Cramer's Rule. Then use Gaussian elimination to solve the system. 4x - 3y - 2z = 12 8x - 6y - 4z = 22

209

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

165

views

Textbook Question

Solve each equation. = 8

130

views

Textbook Question

Solve each equation. = 2x

155

views

Textbook Question

Evaluate each determinant in Exercises 49–52. 4 2 8 - 7 - 2 0 4 1 5 0 0 5 4 0 0 - 1

201

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

194

views

Textbook Question

Evaluate each determinant in Exercises 49–52. 4 2 8 - 7 - 2 0 4 1 5 0 0 5 4 0 0 - 1

201

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

143

views

Textbook Question

Evaluate each determinant in Exercises 49–52. - 2 - 3 3 5 1 - 4 0 0 1 2 2 - 3 2 0 1 1

185

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

193

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

129

views

Textbook Question

In Exercises 46–51, evaluate each determinant.

193

views

Textbook Question

In Exercises 53–54, evaluate each determinant. | | 3 1| |7 0| | | |- 2 3| |1 5| | | | | | 3 0| |9 - 6| | | | 0 7| |3 5| |

183

views

Textbook Question

In Exercises 52–55, use Cramer's Rule to solve each system.

255

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

145

views

Textbook Question

In Exercises 52–55, use Cramer's Rule to solve each system.

255

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

141

views

Textbook Question

In Exercises 55–56, write the system of linear equations for which Cramer's Rule yields the given determinants. 2 - 4 8 - 4 D = D_x = 3 5 - 10 5

434

views

Textbook Question

In Exercises 57–60, solve each equation for x. |- 2 x| | | = 32 | 4 6|

177

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

In Exercises 57–60, solve each equation for x. |1 x - 2| |3 1 1| = - 8 |0 - 2 2|

175

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

136

views

Textbook Question

In Exercises 57–60, solve each equation for x. |1 x - 2| |3 1 1| = - 8 |0 - 2 2|

175

views

Textbook Question

Use the determinant theorems to evaluate each determinant. See Example 4.

128

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. x + y = 4 2x - y = 2

260

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 4x + 3y = -7 2x + 3y = -11

125

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 5x + 4y = 10 3x - 7y = 6

144

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 1.5x + 3y = 5 2x + 4y = 3

139

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 3x + 2y = 4 6x + 4y = 8

127

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. (1/2)x + (1/3)y = 2 (3/2)x - (1/2)y = -12

175

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. 2x - y + 4z = -2 3x + 2y - z = -3 x + 4y + 2z = 17

183

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. x + 2y + 3z = 4 4x + 3y + 2z = 1 -x - 2y - 3z = 0

201

views

Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7. -2x - 2y + 3z = 4 5x + 7y - z = 2 2x + 2y - 3z = -4

163

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 0 - 2 1 1 2 0 3 - 1 0 1 1 0 1 1 1 A = B = 0 1 - 1 0 0 1 0 1 1 0 0 - 1 1 2 0 2

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 1 2 3 7/2 - 3 1/2 A = 1 3 4 B = - 1/2 0 1/2 1 4 3 - 1/2 1 - 1/2

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 0 1 0 0 0 1 A = 0 0 1 B = 1 0 0 1 0 0 0 1 0

133

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. w - x + 2y = - 3 x - y + z = 4 - w + x - y + 2z = 2 - x + y - 2z = - 4 The inverse of is

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. x - y + z = 8 2y - z = - 7 2x + 3y = 1 The inverse of is

views

Textbook Question

In Exercises 37 - 42, a. Write each linear system as a matrix equation in the form AX = B. b. Solve the system using the inverse that is given for the coefficient matrix. 2x + 6y + 6z = 8 2x + 7y + 6z = 10 2x + 7y + 7z = 9 The inverse of is

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 2 1 1 2 A = B = 3/2 - 1/2 3 4

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. - 4 0 - 2 4 A = B = 1 3 0 1

views

Textbook Question

In Exercises 1 - 12, find the products AB and BA to determine whether B is the multiplicative inverse of A. 4 - 3 4 3 A = B = - 5 4 5 4

views

Textbook Question

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

views

Textbook Question

In Exercises 33 - 36, write each matrix equation as a system of linear equations without matrices.

views

Textbook Question

In Exercises 29 - 32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. x + 3y + 4z = - 3 x + 2y + 3z = - 2 x + 4y + 3z = - 6

103

views

Textbook Question

In Exercises 29 - 32, write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix. 6x + 5y = 13 5x + 4y = 10

106

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 10 - 2 A = - 5 1

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 3 - 1 A = - 4 2

views

Textbook Question

In Exercises 13 - 18, use the fact that if a b d - b A = then A^(-1) = 1/(ad-bc) to find the inverse of c d - c a each matrix, if possible. Check that AA^(-1) = I_2 and A^(-1)A = I_2. 2 3 A = - 1 2

views

Textbook Question

In Exercises 43–44, (a) Write each linear system as a matrix equation in the form AX = B (b) Solve the system using the inverse that is given for the coefficient matrix.

views

Textbook Question

In Exercises 39–42, find A^(-1) Check that AA^-1 = I and A^(-1)A = I

views

Textbook Question

In Exercises 37–38, find the products and to determine whether B is the multiplicative inverse of A.

views

Textbook Question

Answer each question. What is the product of [2x2 matrix] and I2 (in either order)?

views

Textbook Question

Answer each question. What is the product [3x3 matrix] [3x3 matrix]?

views

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [2x2 matrix] and [2x2 matrix]

views

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I￬n.) [3x3 matrix] and [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [2x2 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Textbook Question

Find the inverse, if it exists, for each matrix. [3x3 matrix]

views

Showing 115 of 115 practice

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Learn with Patrick

Learn with other creators

Practice this topic